Multiply the following complex numbers: $({-5+5i}) \cdot ({3i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5+5i}) \cdot ({3i}) = $ $ ({-5} \cdot {0}) + ({-5} \cdot {3}i) + ({5}i \cdot {0}) + ({5}i \cdot {3}i) $ Then simplify the terms: $ (0) + (-15i) + (0i) + (15 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (-15 + 0)i + 15i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (-15 + 0)i - 15 $ The result is simplified: $ (0 - 15) + (-15i) = -15-15i $